Statistical diffusion simulation

Same procedure is adopted as the statistical diffusion simulation in SIMION 7.0. The result is added to Axe by Equation 4.1 and ions with x lying inside an electrode are identified. As those ions have hit an electrode, they are removed from simulation and CTq in Equation 4.2 is adjusted. ... 

As explained In Section 1 three dlffuslvltles were calculated for each system. These were the equilibrium transverse dlffuslvlty and the two nonequilibrium (flow) dlffuslvltles parallel and normal to the direction of flow. As we can see from Table I, they all agree with each other within the limits of statistical uncertainty. We conclude, therefore, that the flow has no effect on the diffusivity even at such high shear rates as the ones employed in our simulation. At even higher shear rates a significant dependence of the dlffuslvlty on the shear rate has been reported (Ifl.) but one should consider that our shear rate Is already orders of magnitude higher than the ones encountered In realistic flow situations. 

There are two other methods in which computers can be used to give information about defects in solids, often setting out from atomistic simulations or quantum mechanical foundations. Statistical methods, which can be applied to the generation of random walks, of relevance to diffusion of defects in solids or over surfaces, are well suited to a small computer. Similarly, the generation of patterns, such as the aggregation of atoms by diffusion, or superlattice arrays of defects, or defects formed by radiation damage, can be depicted visually, which leads to a better understanding of atomic processes. 

For simple flows where the mean velocity and/or turbulent diffusivity depend only weakly on the spatial location, the Eulerian PDF algorithm described above will perform adequately. However, in many flows of practical interest, there will be strong spatial gradients in turbulence statistics. In order to resolve such gradients, it will be necessary to use local grid refinement. This will result in widely varying values for the cell time scales found from (7.13). The simulation time step found from (7.15) will then be much smaller than the characteristic cell time scales for many of the cells. When the simulation time step is applied in (7.16), one will find that Ni must be made unrealistically large in order to satisfy the constraint that Nf > 1 for all k. 

MD calculations may be used not only to gain important insight into the microscopic behavior of the system but also to provide quantitative information at the macroscopic level. Different statistical ensembles may be generated by fixing different combinations of state variables, and, from these, a variety of structural, energetic, and dynamic properties may be calculated. For simulations of diffusion in zeolites by MD methods, it is usual to obtain estimates of the diffusion coefficients, D, from the mean square displacement (MSD) of the sorbate, (rfy)), using the Einstein relationship (/) ... 

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